Limit analysis of multispan masonry bridges including arch-fill interaction

The limit analysis of masonry bridges is tackled by considering the interaction between arches, piers and fill. A two-dimensional FE model is defined in which arches and piers are described as beams made of no tensile resistant (NTR), ductile in compression material, and the fill as a heavy rigid-plastic material under plane strain conditions. Increasing pressure distributions are applied to the upper surface of the fill and upper bounds of the collapse load multiplier are obtained by the kinematic theorem. The fill is modelled by triangular constant strain rate elements and the arches and piers by two noded beams. In order to take into account possible discontinuities in the velocity field in the fill, four noded rigid-plastic interfaces are located between the triangular elements. Once linearized the limit domains in the generalised stress space, tangent to the effective limit domain, a linear programming problem is formulated and upper bounds of the collapse loads are obtained. Two examples are analysed and discussed from which the relevant effects of the fill on the collapse mechanism and multiplier are shown; finally, the sensitivity of the collapse multiplier on both the cohesion parameter and the angle of internal friction is obtained